Speaker: Masoud Nasari (Carleton University)

Title: Pivots for the Mean with Negligible Skewness

Date: November 14, 2014

Time: 1:30 pm – 2:30 pm

Room: 4351 HP (Macphail room)

ABSTRACT: In this talk we introduce a broad class of randomized versions of the Student t-statistic, the classical pivot for the mean $\mu$, that continue to possess the pivotal property for $\mu$ and their skewness can be taken to be arbitrary small for each $\emph{fixed}$ sample size $n$. Due to the negligibility of their skewness, these randomized pivots admit CLTs that, under some conventional conditions, are already accurate of the second order.

The introduced randomization framework provides an explicit relation between the accuracy of the CLTs for the randomized pivots and the length of their associated confidence intervals. This property allows regulating the trade-off between the accuracy and the length of the resulting randomized confidence intervals. Our error reduction techniques do not require re-sampling from the data. Consequently, they are not computationally demanding nor are they affected by the error resulting from drawing an insufficiently large number of sub-samples.